Shrinking targets for the geodesic flow on geometrically finite hyperbolic manifolds

DOI10.3934/jmd.2021014zbMath1501.37003arXiv1812.05251OpenAlexW3206869737MaRDI QIDQ2153351

Yanyan Li

Publication date: 4 July 2022

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05251

zbMATH Keywords

hyperbolic manifoldsshrinking targets

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Hyperbolic groups and nonpositively curved groups (20F67) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Homogeneous flows (37A17)

Related Items (5)

Isolations of geodesic planes in the frame bundle of a hyperbolic 3-manifold ⋮ Cohomology fractals, Cannon–Thurston maps, and the geodesic flow ⋮ Multiple Borel-Cantelli lemma in dynamics and multilog law for recurrence ⋮ Effective equidistribution of horospherical flows in infinite volume rank-one homogeneous spaces ⋮ Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps

Cites Work

• Unnamed Item
• On the almost sure spiraling of geodesics in negatively curved manifolds
• Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics
• The density at infinity of a discrete group of hyperbolic motions
• The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces
• Poincaré series of finite geometric groups
• Shrinking targets for discrete time flows on hyperbolic manifolds
• Logarithm laws for flows on homogeneous spaces
• Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds
• Matrix coefficients, counting and primes for orbits of geometrically finite groups
• Closed geodesics and holonomies for Kleinian manifolds
• Geometrical finiteness for hyperbolic groups
• Dynamical Borel-Cantelli lemma for hyperbolic spaces
• An application of lattice points counting to shrinking target problems
• Dimension and hitting time in rapidly mixing systems
• Spectra of Ruelle transfer operators for Axiom A flows
• Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds
• Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds
• Hitting time in regular sets and logarithm law for rapidly mixing dynamical systems
• Hausdorff dimension and conformal dynamics, III: Computation of dimension
• Limit sets of discrete groups of isometries of exotic hyperbolic spaces
• Ergodicité et équidistribution en courbure négative
• The Patterson Measure for Geometrically Finite Groups with Parabolic Elements, New and Old
• Exponential mixing of frame flows for convex cocompact hyperbolic manifolds
• Shrinking target problems for flows on homogeneous spaces
• Shrinking targets for semisimple groups

This page was built for publication: Shrinking targets for the geodesic flow on geometrically finite hyperbolic manifolds